The next update isn't released yet, but should include performance improvements for even the launch Xbox 1 console. So I am starting this topic thread for any specific XBOX issues, questions, or performance issues when game is in release 0.6.8.0. Keep your game saves and retest their performance after the performance update is released.
For me personally, my 2nd save experiences massive lag as soon as I step off, drive off or rise above the original base area. I have a large leveled area surrounding my base and I can move about freely there. Once i go below, or off of the leveled area, and if I'm carrying anything, driving a rover or doing anything but running, I get a massive amount of lag. I have posted a 15 second video of what I'm talking about in the Discord #media section. That video is also attached to this post.
Astroneer is a great game, and I love that it is a Windows Play Anywhere title. I have nothing but praise for the game, and even this lag is the first I've seen in one of my single player XB1 games.
ASTRONEER (Game Preview) (2).mp4

I saw Astroneer first on the XB1, as a free preview. I decided to buy and gifted a copy to my son. I have a Windows 10 computer and my XB1 so I was also VERY HAPPY for the cross platform support. The first version I downloaded (was 0.5.0.0) was awesome and have not stopped playing since. But I have to say that using version 0.6.0.0, it's an even better game. I really enjoy not having to start over, I can use my saves (with a few minor glitches) and it's awesome playing with the new base building features and not having to spend time researching for bytes. But I have also started new games for the multiplayer experience and that has been awesome as well. Keep up the great work, System Era!

I've been impressed by his continued commitment and seemingly doesn't need to sleep. The Astroneer server is by far the most advanced and active server I've joined thus far. Keep up the great effort, @Wyvyrias

@Sir_JellyMan, put fuel in it and take off, or use dynamite to blow it up. You'll need to wait until you see your home base again before landing, or you won't be close to your home base. Click the light blue circle area closest to your home base on the planet. Don't click the orange tab you clicked to take off, that will take you out of orbit around your planet!

@Bel_Riose, for Q#2, at the Main Menu, above your saved game, is a trash can icon. On XB1, use joystick or directional up arrow to select it, then click A. After that, you'll need to click A again to confirm the deletion.

After uninstalling the game, and then reinstalling it, while keeping my game save data, I was able to load my first and longest played game, and the save updated correctly! So I can now access and get updated saves on both my games! FYI, my game is installed on my external 2 TB, the game saves are on my Internal. I can't move my game saves to external. Originally, my first install was on the internal, my second was on the external. Now both updates were installed on the external. Hope that makes sense. Thank you for your reply!

I'm using an Xbox One, so I have only one save game per Astroneer. I cannot select a different (earlier) save game, as of now, as far as I know.
I uninstalled my game on XB1 and reinstalled it. Oddly it only shows as 1.7 GB, but should be 3.2 GB after the 0.5.1.0 update. Anyway, I'm also happy to report that I can now get saves to update for the game I had played before and the game I played after the 0.5.1.0 update! Yeah!

After returning from off planet, I watched my four vehicle train fall into the caves, got stuck on the roof, and after I used the terrain gun to get them down, when I went to jump in the vehicle, all four vehicles in the train and my Astroneer got ejected or fell through the planet (Terran) and into deep space. Then my dude fell back to Terran, and died on impact (expected). I had just returned from off world (Arrid) and had brought back a huge supply of titanium, copper and lithium. Here's the video.
Lost my four vehicles in space!!!!!!?(15 MB).mp4

Well, I just tried to save my game again. Last good save was made on Jan 15, 2018 at 8:45 pm. That's also shortly after my four vehicles fell into the caves, got stuck on the roof, and after I used the terrain gun to get them down, when I went to jump in the vehicle, all four vehicles in the train and my Astroneer got ejected or fell through the planet (Terran) and into deep space. Then my dude fell back to Terran, and died on impact (expected). I had just returned from off world (Arrid) and had brought back a huge supply of titanium, copper and lithium. Since then, it dumps me back to the save on Arrid, on the above date. I've played several hours in that game since, and every save says "Saving Game", yet the date or time doesn't change, and it also takes me back to the same exact spot on Arrid. As I posted before, save file on XB1 is 19.8 MB.